'Dr. Urth,' said Davenport, 'will you give us your analysis?'

'Ah! Well, all right.' The little extraterrologist settled back in his chair and mopped his damp forehead on his sleeve. 'Let's consider the message. If you accept the quartered circle and the arrow as directing you to me, that leaves seven items. If these indeed refer to seven craters, six of them, at least, must be designed merely to distract, since the Device surely cannot be in more than one place. It contained no movable or detachable parts-it was all one piece.

'Then, too, none of the items are straightforward. SU might, by your interpretation, mean any place on the other side of the Moon, which is an area the size of South America. Again PC/2 can mean "Tycho," as Mr. Ashley says, or it can mean "halfway between Ptolemaeus and Copernicus," as Mr. Davenport thought, or for that matter "halfway between Plato and Cassini." To be sure, XY2 could mean "Alfonsus"-very ingenious interpretation, that-but it could refer to some coordinate system in which the Y coordinate was the square of the X coordinate. Similarly C-C would mean "Bond" or it could mean "halfway between Cassini and Copernicus." F/A could mean "Newton" or it could mean "between Fabricius and Archimedes."

'In short, the items have so many meanings that they are meaningless. Even if one of them had meaning, it could not be selected from among the others, so that it is only sensible to suppose that all the items are merely red herrings.

'It is necessary, then, to determine what about the message is completely unambiguous, what is perfectly clear. The answer to that can only be that it is a message, that it is a clue to a hiding place. That is the one thing we are certain about isn't it ?'

Davenport nodded, then said cautiously, 'At least, we think we are certain of it.'

'Well, you have referred to this message as the key to the whole matter. You have acted as though it were the crucial clue. Jennings himself referred to the Device as a key or a clue. If we combine this serious view of the matter with Jennings' penchant for puns, a penchant which may have been heightened by the mind-tampering Device he was carrying---So let me tell you a story.

'In the last half of the sixteenth century, there lived a German Jesuit in Rome. He was a mathematician and astronomer of note and helped Pope Gregory XIII reform the calendar in 1582, performing all the enormous calculations required. This astronomer admired Copernicus but he did not accept the heliocentric view of the Solar System. He clung to the older belief that the Earth was the center of the Universe.

'In 1650, nearly forty years after the death of this mathematician, the Moon was mapped by another Jesuit, the Italian astronomer, Giovanni Battista Riccioli. He named the craters after astronomers of the past and since he too rejected Copernicus, he selected the largest and most spectacular craters for those who placed the Earth at the center of the Universe-for Ptolemy, Hipparchus, Alfonso X, Tycho Brahe. The biggest crater Riccioli could find he reserved for his German Jesuit predecessor.

This crater is actually only the second largest of the craters visible from Earth. The only larger crater is Bailly, which is right on the Moon's limb and is therefore very difficult to see from the Earth. Riccioli ignored it, and it was named for an astronomer who lived a century after his time and who was guillotined during the French Revolution.'

Ashley was listening to all this restlessly. 'But what has this to do with the message?'

'Why, everything,' said Urth, with some surprise. 'Did you not call this message the key to the whole business? Isn't it the crucial clue?'

'Yes, of course.'

'Is there any doubt that we are dealing with something that is a clue or key to something else?'

'No, there isn't,' said Ashley.

'Well, then---The name of the German Jesuit I have been speaking of is Christoph Klau-pronounced "klow." Don't you see the pun ? Klau-clue ?'

Ashley's entire body seemed to grow flabby with disappointment. 'Farfetched,' he muttered.

Davenport said anxiously, 'Dr. Urth, there is no feature on the Moon named Klau as far as I know.'

'Of course not,' said Urth excitedly. That is the whole point. At this period of history, the last half of the sixteenth century, European scholars were Latinizing their names. Klau did so. In place of the German "u", he made use of the equivalent letter, the Latin "v". He then added an "ius" ending typical of Latin names and Christoph Klau became Christopher Clavius, and I suppose you are all aware of the giant crater we call Clavius.'

'But--' began Davenport.

'Don't "but" me,' said Urth. 'Just let me point out that the Latin word "clavis" means "key." Now do you see the double and bilingual pun? Klau-clue, Clavius-clavis- key. In his whole life, Jennings could never have made a double, bilingual pun, without the Device. Now he could, and I wonder if death might not have been almost triumphant under the circumstances. And he directed you to me because he knew I would remember his penchant for puns and because he knew I loved them too.'

The two men of the Bureau were looking at him wide-eyed.

Urth said solemnly, 'I would suggest you search the shaded rim of Clavius, at that point where the Earth is nearest the zenith.'

Ashley rose. 'Where is your videophone ?'

'In the next room."

Ashley dashed. Davenport lingered behind. 'Are you sure. Dr. Urth?'

'Quite sure. But even if I am wrong, I suspect it doesn't matter.'

'What doesn't matter ?'

'Whether you find it or not. For if the Ultras find the Device, they will probably be unable to use it.'

'Why do you say that ?'

"You asked me if Jennings had ever been a student of mine, but you never asked me about Strauss, who was also a geologist. He was a student of mine a year or so after Jennings. I remember him well.'

'Oh?'

'An unpleasant man. Very cold. It is the hallmark of the Ultras, I think. They are all very cold, very rigid, very sure of themselves. They can't empathize, or they wouldn't speak of killing off billions of human beings. What emotions they possess are icy ones, self-absorbed ones, feelings incapable of spanning the distance between two human beings.'

'I think I see.'

'I'm sure you do. The conversation reconstructed from Strauss's ravings showed us he could not manipulate the Device. He lacked the emotional intensity, or the type of necessary emotion. I imagine all Ultras would. Jennings, who was not an Ultra, could manipulate it. Anyone who could use the Device would, I suspect, be incapable of deliberate cold-blooded cruelty. He might strike out of panic fear as Jennings struck at Strauss, but never out of calculation, as Strauss tried to strike at Jennings. In short, to put it tritely, I think the Device can be actuated by love, but never by hate, and the Ultras are nothing if not haters.'

Davenport nodded. 'I hope you're right. But then-why were you so suspicious of the government's motives if you felt the wrong men could not manipulate the Device?'

Urth shrugged. 'I wanted to make sure you could bluff and rationalize on your feet and make yourself convincingly persuasive at a moment's notice. After all, you may have to face my niece.'

Foreword.

This story has even pleasanter memories for me than the one before. At the Twenty-fourth World Science Fiction Convention, held in Cleveland over the Labor Day weekend in 1966, I was one of those who received a Hugo (the 'Oscar' of science fiction fandom), under conditions of great satisfaction to myself, and with my wife and children in the audience to see. (I am grinning foolishly for sheer joy of recall as I type this.) The science fiction magazine IF also won a Hugo and its editor set about collecting promises from other Hugo winners to write stories for a special Hugo issue. I would have had to have a heart of obsidian not to promise-so I did. This is the result. It is the only story I know of to combine the mystery form with Einstein's General Theory of Relativity.

The Billiard Ball.

James Priss-I suppose I ought to say Professor James Priss, though everyone is sure to know whom I mean even without the tide-always spoke slowly.

I know. I interviewed him often enough. He had the greatest mind since Einstein, but it didn't work quickly. He admitted his slowness often. Maybe it was because he had so great a mind that it didn't work quickly.

He would say something in slow abstraction, then he would think, and then he would say something more. Even over trivial matters, his giant mind would hover uncertainly, adding a touch here and then another there.

Would the Sun rise tomorrow, I can imagine him wondering. What do we mean by 'rise'? Can we be certain that tomorrow will come? Is the term 'Sun' completely unambiguous in this connection ?

Add to this habit of speech a bland countenance, rather pale, with no expression except for a general look of uncertainty; gray hair, rather thin, neatly combed; business suits of an invariably conservative cut; and you have what Professor James Priss was-a retiring person, completely lacking in magnetism.

That's why nobody in the world, except myself, could possibly suspect him of being a murderer. And even I am not sure. After all, he was slow-thinking; he was always slow-thinking. Is it conceivable that at one crucial moment he managed to think quickly and act at once ?

It doesn't matter. Even if he murdered, he got away with it. It is far too late now to try to reverse matters and I wouldn't succeed in doing so even if I decided to let this be published Edward Bloom was Priss's classmate in college, and an associate, through circumstance, for a generation afterward. They were equal in age and in their propensity for the bachelor life, but opposites in everything else that mattered.

Bloom was a living flash of light; colorful, tall, broad, loud, brash, and self-confident. He had a mind that resembled a meteor strike in the sudden and unexpected way it could seize the essential. He was no theoretician, as Priss was; Bloom had neither the patience for it, nor the capacity to concentrate intense thought upon a single abstract point. He admitted that; he boasted of it.

What he did have was an uncanny way of seeing the application of a theory; of seeing the manner in which it could be put to use. In the cold marble block of abstract structure, he could see, without apparent difficulty, the intricate design of a marvelous device. The block would fall apart at his touch and leave the device.

It is a well-known story, and not too badly exaggerated, that nothing Bloom ever built had failed to work, or to be patentable, or to be profitable. By the time he was forty-five, he was one of the richest men on Earth.

And if Bloom the Technician were adapted to one particular matter more than anything else, it was to the way of thought of Priss the Theoretician. Bloom's greatest gadgets were built upon Priss's greatest thoughts, and as Bloom grew wealthy and famous, Priss gained phenomenal respect among his colleagues.

Naturally it was to be expected that when Priss advanced his Two-Field Theory, Bloom would set about at once to build the first practical anti-gravity device.

My job was to find human interest in the Two-Field Theory for the subscribers to Tele-News Press, and you get that by trying to deal with human beings and not with abstract ideas. Since my interviewee was Professor Priss, that wasn't easy.

Naturally, I was going to ask about the possibilities of anti-gravity, which interested everyone; and not about the Two-Field Theory, which no one could understand.

'Anti-gravity?' Priss compressed his pale lips and considered. 'I'm not entirely sure that it is possible, or ever will be. I haven't-uh-worked the matter out to my satisfaction. I don't entirely see whether the Two-Field equations would have a finite solution, which they would have to have, of course, if-'-' And then he went off into a brown study.

I prodded him. 'Bloom says he thinks such a device can be built.'

Priss nodded. 'Well, yes, but I wonder. Ed Bloom has had an amazing knack at seeing the unobvious in the past. He has an unusual mind. It's certainly made him rich enough.'

We were sitting in Priss's apartment. Ordinary middle-class. I couldn't help a quick glance this way and that. Priss was not wealthy.

I don't think he read my mind. He saw me look. And I think it was on his mind. He said, 'Wealth isn't the usual reward for the pure scientist. Or even a particularly desirable one.'

Maybe so, at that, I thought. Priss certainly had his own kind of reward. He was the third person in history to win two Nobel Prizes, and the first to have both of them in the sciences and both of them unshared. You can't complain about that. And if he wasn't rich, neither was he poor.

But he didn't sound like a contented man. Maybe it wasn't Bloom's wealth alone that irked Priss; maybe it was Bloom's fame among the people of Earth generally; maybe it was the fact that Bloom was a celebrity wherever he went, where as Priss, outside scientific conventions and faculty clubs, was largely anonymous.

I can't say how much of all this was in my eyes or in the way I wrinkled the creases in my forehead, but Priss went on to say, 'But we're friends, you know. We play billiards once or twice a week. I beat him regularly.'

(I never published that statement. I checked it with Bloom, who made a long counterstatement that began: 'He beats me at billiards. That jackass---' and grew increasingly personal thereafter. As a matter of fact, neither one was a novice at billiards. I watched them play once for a short while, after the statement and counterstatement, and both handled the cue with professional aplomb. What's more, both played for blood, and there was no friendship in the game that I could see.) I said, 'Would you care to predict whether Bloom will manage to build an anti-gravity device?'

'You mean would I commit myself to anything? Hmm. Well, let's consider, young man. Just what do we mean by anti-gravity? Our conception of gravity is built around Einstein's General Theory of Relativity, which is now a century and a half old but which, within its limits, remains firm. We can picture it---'

I listened politely. I'd heard Priss on the subject before, but if I was to get anything out of him-which wasn't certain-I'd have to let him work his way through in his own way.

'We can picture it,' he said, 'by imagining the Universe to be a flat, thin, superflexible sheet of untearable rubber. If we picture mass as being associated with weight, as it is on the surface of the Earth, then we would expect a mass, resting upon the rubber sheet, to make an indentation. The greater the mass, the deeper the indentation.

'In the actual Universe,' he went on, 'all sorts of masses exist, and so our rubber sheet must be pictured as riddled with indentations. Any object rolling along the sheet would dip into and out of the indentations it passed, veering and changing direction as it did so. It is this veer and change of direction that we interpret as demonstrating the existence of a force of gravity. If the moving object comes close enough to the center of the indentation and is moving slowly enough, it gets trapped and whirls round and round that indentation. In the absence of friction, it keeps up that whirl forever. In other words, what Isaac Newton interpreted as a force, Albert Einstein interpreted as geometrical distortion.'

He paused at this point. He had been speaking fairly fluently-for him-since he was saying something he had said often before. But now he began to pick his way.

He said, 'So in trying to produce anti-gravity, we are trying to alter the geometry of the Universe. If we carry on our metaphor, we are trying to straighten out the indented rubber sheet. We could imagine ourselves getting under the indenting mass and lifting it upward, supporting it so as to prevent it from making an indentation. If we make the rubber sheet flat in that way, then we create a Universe-or at least a portion of the Universe-in which gravity doesn't exist. A rolling body would pass the non-indenting mass without altering its direction of travel a bit, and we could interpret this as meaning that the mass was exerting no gravitational force. In order to accomplish this feat, however, we need a mass equivalent to the indenting mass. To produce anti-gravity on Earth in this way, we would have to make use of a mass equal to that of Earth and poise it above our heads, so to speak.'

I interrupted him. 'But your Two-field Theory---'

'Exactly. General Relativity does not explain both the gravitational field and the electromagnetic field in a single set of equations. Einstein spent half his life searching for that single set-for a Unified Field Theory-and failed. All who followed Einstein also failed. I, however, began with the assumption that there were two fields that could not be unified and followed the consequences, which I can explain, in part, in terms of the "rubber sheet" metaphor.'

Now we came to something I wasn't sure I had ever heard before. 'How does that go?' I asked.

'Suppose that, instead of trying to lift the indenting mass, we try to stiffen the sheet itself, make it less indentable. It would contract, at least over a small area, and become flatter. Gravity would weaken, and so would mass, for the two are essentially the same phenomenon in terms of the indented Universe. If we could make the rubber sheet completely flat, both gravity and mass would disappear altogether.

'Under the proper conditions, the electromagnetic field could be made to counter the gravitational field, and serve to stiffen the indented fabric of the Universe. The electromagnetic field is tremendously stronger than the graviational field, so the former could be made to overcome the latter.'

I said uncertainly, 'But you say "under the proper conditions." Can those proper conditions you speak of be achieved. Professor?'

That is what I don't know,' said Priss thoughtfully and slowly. 'If the Universe were really a rubber sheet, its stiffness would have to reach an infinite value before it could be expected to remain completely flat under an indenting mass. If that is also so in the real Universe, then an infinitely intense electromagnetic field would be required and that would mean anti-gravity would be impossible.'

'But Bloom says---'

'Yes, I imagine Bloom thinks a finite field will do, if it can be properly applied. Still, however ingenious he is,' and Priss smiled narrowly, 'we needn't take him to be infallible. His grasp on theory is quite faulty. He-he never earned his college degree, did you know that?'

I was about to say that I knew that. After all, everyone did. But there was a touch of eagerness in Priss's voice as he said it and I looked up in time to catch animation in his eye, as though he were delighted to spread that piece of news. So I nodded my head as if I were filing it for future reference.

Then you would say, Professor Priss,' I prodded again, 'that Bloom is probably wrong and that anti-gravity is impossible?'

And finally Priss nodded and said, The gravitational field can be weakened, of course, but if by anti-gravity we mean a true zero-gravity field-no gravity at all over a significant volume of space-then I suspect anti-gravity may turn out to be impossible, despite Bloom.'

And I had, after a fashion, what I wanted.

I wasn't able to see Bloom for nearly three months after that, and when I did see him he was in an angry mood.

He had grown angry at once, of course, when the news first broke concerning Priss's statement. He let it be known that Priss would be invited to the eventual display of the anti-gravity device as soon as it was constructed, and would even be asked to participate in the demonstration. Some reporter-not I, unfortunately-caught him between appointments and asked him to elaborate on that and he said: 'I'll have the device eventually; soon, maybe. And you can be there, and so can anyone else the press would care to have there. And Professor James Priss can be there. He can represent Theoretical Science and after I have demonstrated anti-gravity, he can adjust his theory to explain it. I'm sure he will know how to make his adjustments in masterly fashion and show exactly why I couldn't possibly have failed. He might do it now and save time, but I suppose he won't.'

It was all said very politely, but you could hear the snarl under the rapid flow of words.

Yet he continued his occasional game of billiards with Priss and when the two met they behaved with complete propriety. One could tell the progress Bloom, was making by their respective attitudes to the press. Bloom grew curt and even snappish, while Priss developed an increasing good humor.

When my umpteenth request for an interview with Bloom was finally accepted, I wondered if perhaps that meant a break in Bloom's quest. I had a little daydream of him announcing final success to me. It didn't work out that way. He met me in his office at Bloom Enterprises in upstate New York. It was a wonderful setting, well away from any populated area, elaborately landscaped, and covering as much ground as a rather large industrial establishment. Edison at his height, two centuries ago, had never been as phenomenally successful as Bloom.

But Bloom was not in a good humor. He came striding in ten minutes late and went snarling past his secretary's desk with the barest nod in my direction. He was wearing a lab coat, unbuttoned.

He threw himself into his chair and said, 'I'm sorry if I've kept you waiting, but I didn't have as much time as I had hoped.' Bloom was a born showman and knew better than to antagonize the press, but I had the feeling he was having a great deal of difficulty at that moment in adhering to this principle.

I made the obvious guess. 'I am given to understand, sir, that your recent tests have been unsuccessful.'

'Who told you that ?'

'I would say it was general knowledge, Mr. Bloom.'

'No, it isn't. Don't say that, young man. There is no general knowledge about what goes on in my laboratories and workshops. You're stating the Professor's opinions, aren't you ? Priss's, I mean.'

'No I'm--'

'Of course you are. Aren't you the one to whom he made that statement-that anti-gravity is impossible?'

'He didn't make the statement that flatly.'

'He never says anything flatly, but it was flat enough for him, and not as flat as I'll have his damned rubber-sheet Universe before I'm finished.'